Wireless Networks with Asynchronous Users

This paper addresses an interference channel consisting of $\mathbf{n}$ active users sharing $u$ frequency sub-bands. Users are asynchronous meaning there exists a mutual delay between their transmitted codes. A stationary model for interference is considered by assuming the starting point of an interferer's data is uniformly distributed along the codeword of any user. This model is not ergodic, however, we show that the noise plus interference process satisfies an Asymptotic Equipartition Property (AEP) under certain conditions. This enables us to define achievable rates in the conventional Shannon sense. The spectrum is divided to private and common bands. Each user occupies its assigned private band and the common band upon activation. In a scenario where all transmitters are unaware of the number of active users and the channel gains, the optimum spectrum assignment is obtained such that the so-called outage capacity per user is maximized. If $\Pr\{\mathbf{n}>2\}>0$, all users follow a locally Randomized On-Off signaling scheme on the common band where each transmitter quits transmitting its Gaussian signals independently from transmission to transmission. Achievable rates are developed using a conditional version of Entropy Power Inequality (EPI) and an upper bound on the differential entropy of a mixed Gaussian random variable. Thereafter, the activation probability on each transmission slot together with the spectrum assignment are designed resulting in the largest outage capacity.